% FPI for nonlinear equations system.
% Input: g1, g2, g3 are functions, x0 - initial vector, eps -tolerance
% Output: x - solution and s - iteration number, and forerr - ||xk-xk-1||
function[x forerr s]=fpimulti(g1,g2,g3,x0,eps)
s=1; 
x(1,:)=x0; forerr1(s)=1;
while norm(forerr1(s),inf)>eps
    s=s+1;
    x(s,1)=g1(x(s-1,1),x(s-1,2),x(s-1,3));
    x(s,2)=g2(x(s-1,1),x(s-1,2),x(s-1,3));
    x(s,3)=g3(x(s-1,1),x(s-1,2),x(s-1,3));
    forerr1(s)=norm(x(s,:)-x(s-1,:),inf);
end
forerr=forerr1';
___________________________________________________________________________
format long
eps=10^(-7); x0=[0.1;0.1;-0.1];
g1=inline('(1/3)*cos(z*y)+1/6+x-x');
g2=inline('(1/9)*sqrt(x^2+sin(z)+1.06)-0.1+y-y');
g3=inline('-exp(x*y)/20-(10*pi-3)/60+z-z');
[x forerr step]=fpimulti(g1,g2,g3,x0,eps)

x =

   0.100000000000000   0.100000000000000  -0.100000000000000
   0.499983333472222   0.009441149603713  -0.523101267285757
   0.499995934919313   0.000025567746767  -0.523363310908805
   0.499999999970157   0.000012336720363  -0.523598136413912
   0.499999999993046   0.000000034167906  -0.523598467181241
   0.500000000000000   0.000000016487040  -0.523598774744101
   0.500000000000000   0.000000000045664  -0.523598775186123


forerr =

   1.000000000000000
   0.423101267285757
   0.009415581856947
   0.000234825505107
   0.000012302552457
   0.000000307562860
   0.000000016441376


step =

     7
___________________________________________________________________________
% Seidel Method for nonlinear equations system.
% Input: g1, g2, g3 are functions, x0 - initial vector, eps -tolerance
% Output: x - solution and s - iteration number, and forerr - ||xk-xk-1||
function[x forerr s]=seidelmulti(g1,g2,g3,x0,eps)
s=1; 
x(1,:)=x0; forerr1(s)=1;
while norm(forerr1(s),inf)>eps
    s=s+1;
    x(s,1)=g1(x(s-1,1),x(s-1,2),x(s-1,3));
    x(s,2)=g2(x(s,1),x(s-1,2),x(s-1,3));
    x(s,3)=g3(x(s,1),x(s,2),x(s-1,3));
    forerr1(s)=norm(x(s,:)-x(s-1,:),inf);
end
forerr=forerr1';
___________________________________________________________________________
[x forerr step]=seidelmulti(g1,g2,g3,x0,eps)

x =

   0.100000000000000   0.100000000000000  -0.100000000000000
   0.499983333472222   0.022229793558577  -0.524157601703545
   0.499977372401068  -0.000031270728399  -0.523597993871579
   0.499999999955319   0.000000041787070  -0.523598776642975
   0.500000000000000  -0.000000000055847  -0.523598775596903


forerr =

   1.000000000000000
   0.424157601703545
   0.022261064286976
   0.000031312515468
   0.000000041842916


step =

     5